Infrared spectrometry is an accepted and widely practiced technique for identification and quantification of compounds. The most common method of spectrometric analysis utilizes a transmission spectra. In traditional transmission spectrometry, an analysis beam of infrared light is passed through the substance being analyzed. The sample substance absorbs light in varying amounts at different wavelengths producing a transmission spectra which is a graph of the energy passed through the sample vs. wavelength. It will be appreciated that the use of transmission spectrometry generally requires that the substance being analyzed be contained in a "cell" which is placed inside the instrument for scanning. The analysis beam enters one side of the cell and exits the other. This is clearly an in-vitro technique, and is not suitable for non-invasive measurements.
In another common spectrometric technique the phenomena of Attenuated Total Internal Reflection (ATIR) is used. In this technique the sample is deposited on a plate fabricated of infrared transmissive material. The analysis beam is reflected off of this plate and back into the analyzer. At the point of reflection a portion of the analysis beam (evanescence wave) actually travels through the plate and interacts with the sample, then this portion of the beam returns to the analyzer along with the other reflected beam. A 1000 cm-1 infrared ATIR beam typically penetrates 10 microns into the sample under study. This technique, although potentially non-invasive, is not suitable for studying the composition of deeper layers of a material.
Transmission mode measurements are ideal for gasses which transmit a large percentage of incident energy and can be easily contained in a cell. Solids and liquids are traditionally measured by using either very thin transmission mode samples or the ATIR technique. The transmission mode technique has severe limitations if the substance being measured is very dense in the wavelength region of interest. For instance if one was analyzing glucose dissolved in water or human blood the 9 to 10 micron wavelength region would be ideal however the incident analysis beam would be totally absorbed with less than 200 microns of path length. Maintaining a sample of such thin proportions is difficult. In such a case of high absorption, the ATIR technique might be useful, however, in that technique the analysis beam is only probing the surface of the substance being analyzed. The technique is useful only if the properties being measured exist at the surface of the sample.
Transmission and ATIR mode analyses are very useful in the laboratory: however if one wishes to measure something in-vivo, such as glucose in blood where even the most peripheral capillaries are covered by a typical minimum of 40 microns of epithelial tissue, clearly neither technique is adequate.
To enable in-vivo measurement of various analytes, infrared detection has been introduced in several applications. Infrared detection techniques are widely used for the calculation of oxygen saturation and the concentration of other blood constituents. For example, non-invasive pulse oximeters have been used to measure absorption signals at two or more visible and/or near infrared wavelengths and to process the collected data to obtain composite pulsatile flow data of a person's blood. Sample pulse oximeters of this type are described by Corenman et al. in U.S. Pat. No. 4,934,372; by Edgar, Jr. et al. in U.S. Pat. No. 4,714,080; and by Zelin in U.S. Pat. No. 4,819,752.
Infrared detection techniques have also been used to calculate the concentrations of constituents such as nitrous oxide and carbon dioxide in the expired airstream of a patient. For example, Yelderman et al. describe in U.S. Pat. Nos. 5,081,998 and 5,095,913 techniques for using infrared light to non-invasively measure the absolute concentrations of the constituents of the respiratory airstream of a patient by placing an infrared transmission/detection device on the artificial airway of the patient. These infrared detection techniques and those described above have proven to be quite accurate in the determination of arterial blood oxygen saturation, the patient's pulse, and the concentrations of carbon dioxide, nitrous oxide and other respiratory constituents.
Spectrophotometric methods have also been used to non-invasively monitor the oxidative metabolism of body organs in vivo using measuring and reference wavelengths in the near infrared region. For example, Jobsis describes in U.S. Pat. Nos. 4,223,680 and 4,281,645 a technique in which infrared wavelengths in the range of 700-1300 nm are used to monitor oxygen sufficiency in an organ such as the brain or heart of a living human or animal. In addition, Wilber describes in U.S. Pat. No. 4,407,290 a technique in which visible and near infrared light emitting diodes and detection circuitry are used to non-invasively measure changes in blood thickness of predetermined blood constituents relative to total change in blood thickness at a test area so as to determine the concentration of such constituents in the blood. Such constituents include hemoglobin and oxyhemoglobin, and the measured concentrations are used to determine the oxygen saturation of the blood. Wilber further suggests at columns 11-12 that such techniques may be extended to the measurement of glucose in the bloodstream; however, Wilber does not tell how to make such measurements, what wavelengths of energy to use, or the form of the mathematics necessary for the calculation of glucose concentration.
Long wavelength spectroscopic glucose monitoring techniques using infrared light are presently believed to be the most accurate and are the subject of the present application. Unlike the non-invasive oxygen saturation measurement techniques described above, prior art spectroscopic glucose monitoring techniques have typically used extra-corporeal "flow through" cells that allow continuous measurements using infrared light. Indeed, attenuated total internal reflection (ATIR) cells have been employed in the long wavelength infrared to measure the glucose content of extracted blood samples. However, as previously discussed, such techniques require samples of blood to be taken from the person and are thus undesirable for widespread consumer use.
Laser Raman Spectroscopy is another spectroscopic technique which uses a visible spectrum range stimulus and the visible red spectrum for measurement. As with ATIR cells, extra-corporeal blood is also used with Raman Technology. The Raman technique is based upon the principle that if excited with a specific wavelength certain constituents will re-emit optical energy at composition dependent specific wavelengths. Over the entire visible spectrum range whole blood has a high degree of absorption.
Another class of spectroscopic technique is described by Barnes in U.S. Pat. No. 5,070,874. According to this technique, often referred to as non-invasive near infrared spectroscopy, light is passed though a finger or suitable appendage and monitored upon exit for measuring glucose levels in vivo. Unfortunately, this technique suffers from two sources of inaccuracy: tissue interference and lack of specificity. Moreover, while the near infrared wavelengths used are easily and economically generated by light emitting diodes (LEDs) and solid state lasers, and easily transmitted through human tissue, they are not in a range specifically absorbed by glucose. This lack of "fingerprint" absorbance and interference from tissue pigment and condition render the technique unsuitable for accurate concentration determination but possibly acceptable for trending if stability can be maintained.
In an attempt to overcome the limitations of near infrared wavelengths Kaiser describes in Swiss Patent No. 612,271 a technique in which a high power infrared laser is used as the radiation source for measuring glucose concentration in a measuring cell. The measuring cell consists of an ATIR measuring prism which is wetted by the person's blood and an ATIR reference prism which is wetted with a comparison solution. CO.sub.2 laser radiation, typically at 10.5 microns wavelength, is led through the measuring cell and gathered before striking a signal processing device. A chopper placed before the measuring cell allows two voltages to be obtained corresponding to the signal from the sample and the reference prisms.
Due to absorption corresponding to the concentration of the substance measured in the blood, the difference between the resulting voltages is proportional to the concentration. Unfortunately, the infrared laser used by Kaiser needs to be very powerful to get the 10.5 micron energy to pass through the blood and has the undesirable side effect of heating the blood, which may be harmful to the person if the blood were returned to the body. Although Kaiser suggests that over heating the blood may be prevented by using extra-corporeal cuvettes of venous blood and high blood flow rates, Kaiser does not describe a non-invasive technique for measuring glucose concentration.
March in U.S. Pat. No. 3,958,560 describes a "non invasive" automatic glucose sensor system which senses the rotation of polarized near infrared light which has passed through the cornea of the eye. March's glucose sensor fits over the eyeball between the eyelid and the cornea and measures glucose as a function of the amount of radiation detected at the detector on one side of the person's cornea. Unfortunately, while such a technique does not require the withdrawal of blood and is thus "non-invasive", the sensor may cause considerable discomfort to the person because of the need to place it on the person's eye. A more accurate and less intrusive system is desired.
Hutchinson describes in U.S. Pat. No. 5,009,230 a personal glucose monitor which also uses polarized near infrared light to non-invasively detect glucose concentrations in the person's bloodstream. The amount of rotation imparted on the polarized light beam is measured as it passes through a vascularized portion of the body for measuring the glucose concentration in that portion of the body. Although the monitor described by Hutchinson need not be mounted on the person's eye, the accuracy of the measurement is limited by the relatively minimal and non specific absorption of glucose in the 940-1000 nm range, dictated by the requirement of polarization, used by Hutchinson.
Mendelson et al. in U.S. Pat. No. 5,137,023 also found that wavelengths in the near infrared range are useful for non-invasively measuring the concentration of an analyte such as glucose using pulsatile photoplethysmography. In particular, Mendelson et al. describes a glucose measuring instrument which uses the principles of transmission and reflection photoplethysmography, whereby glucose measurement is made by analyzing either the differences or the ratio of two different near infrared radiation sources that are either transmitted through an appendage or reflected from a tissue surface before and after blood volume change occurs in the systolic and diastolic phases of the cardiac cycle. The technique of photoplethysmography can thus be used to adjust the light intensity to account for errors introduced by excessive tissue absorptions. However, despite the assertions by Mendelson et al., the wavelengths in the near infrared (below 2500 nm) are not strongly absorbed by glucose yet are susceptible to interference from other compounds in the blood and thus cannot yield sufficiently accurate measurements.
Rosenthal et al. in U.S. Pat. No. 5,028,787 disclose a non-invasive blood glucose monitor which also uses infrared energy in the near infrared range (600-1100 nm) to measure glucose. However, as with the above-mentioned devices, these wavelengths are not in the primary absorption range of glucose and, accordingly, the absorption at these wavelengths is relatively weak. A more accurate glucose measuring technique which monitors glucose absorption in its primary absorption range is desirable.
As with other molecules, glucose more readily absorbs infrared light at certain frequencies because of the characteristic and essential infrared absorption wavelengths of its covalent bonds. For example, as described by Hendrickson et al. in Organic Chemistry, 3rd Edition, McGraw-Hill Book Company, Chapter 7. Section 7-5, pages 256-264, C--C, C--N, C--O and other single carbon-hydrogen bonds have characteristic absorption wavelengths in the 6.5-15 micron range. Due to the presence of such bonds in glucose, infrared absorption by glucose is particularly distinctive in the far infrared. Despite these characteristics, few have suggested measuring glucose concentration in the middle to far infrared range, likely due to the strong tissue absorption that would attenuate signals in that range.
In one known example of such teachings, Mueller describes in WO 81/00622 a method and device for determining the concentration of metabolites in blood using spectroscopic techniques for wavelengths in the far infrared range. In particular, Mueller teaches the feasibility of measuring glucose in extra-corporeal blood samples using a 9.1 .mu.m absorption wavelength and a 10.5 .mu.m reference wavelength for stabilizing the absorption reading. However, Mueller does not describe how such wavelengths may be used in vivo to measure glucose concentration non-invasively while overcoming the above-mentioned tissue absorption problems. Without overcoming the large absorption by tissue in the 9 to 10 micron wavelength range, typically 90% absorption within about 30 microns of optical path in human tissue, high power infrared energy must be incident on the measurement site which can cause tissue damage and discomfort.
On the other hand, infrared emissions of bodies have been used to determine the absolute temperatures of those bodies. For example, some of the present inventors disclose a tympanic thermometer in U.S. Pat. No. 5,159,936 which measures the absolute temperature of a person from the sum total of all infrared energy emissions from the person's tympanic membrane. However, such broadband infrared energy emissions have not been used to perform constituent composition and concentration analysis.
Another prior art device developed by some of the inventors of the present invention is disclosed in U.S. Pat. No. 5,313,941 by Braig et al. In this device high intensity infrared energy of the optimal wavelength, 3 to 12 microns is passed through the finger to make a transmission mode measurement. This device requires high incident energy levels to overcome the high absorbance of tissue in this wavelength band. In this device the energy is pulsed at very low duty cycles to avoid overheating the skin.
McClelland in U.S. Pat. Nos. 5,070,242; 5,075,552; and 5,191,215 describes a method for applying a cooling medium to cool a thin surface layer portion of the material and to transiently generate a temperature differential between the thin surface layer portion and the lower portion of the material sufficient to alter the thermal infrared emission spectrum of the body from the black-body thermal infrared emission of the material. The altered thermal emission spectrum is detected while the emission spectrum is sufficiently free of self-absorption by the material of the emitted infrared radiation. The detection is effected prior to the temperature differential propagating into the lower portion of the material to an extent such that the altered thermal infrared emission spectrum is no longer sufficiently free of self-absorption by the material of emitted infrared radiation. By such detection, the detected altered thermal infrared emission spectrum is indicative of the characteristics relating to the molecular composition of the homogenous material.
Transient thermal emission spectrometry, for instance as taught by McClelland in U.S. Pat. No. 5,075,552; and by Imhof, (SPIE Vol.2329), is useful for the analysis of surface layer composition. Such spectrometry has also been applied to in-vivo skin research. Heat (in the form of radiation or hot gas) is applied to a surface and an emission spectrum is measured that contains spectral information about molecular composition of several conventional transmission spectrum. Spectra of respectable quality have been obtained by this methodology. Further, depth profiling has been carried out by time-resolved use of a laser at different wavelengths and different thermal penetration depths as a function of time. Radiation intensity is absorbed exponentially with depth leaving much more energy in the surface layers. A significant fraction of the absorbed energy is emitted from that surface layer without being "self-absorbed" again. It is this phenomenon of emission emanating largely from the immediate surface layer, that limits the usefulness of the emission technology to the top surface. This is because these emissions contain only specific spectral content of the top surface layer. Analysis of the deeper layers is also hampered by this, and a second effect: Specific emissions from deeper layers are self-absorbed by the top layers of material closer to the surface and are thereby largely converted to a non-specific blackbody emission. Thus, transient thermal emission spectrometry may be useful for top surface analysis but offers less potential for subsurface layer compositional analysis.
A possible solution to the shortcomings of previous transient thermal emission spectroscopic methodologies as used for subsurface layer compositional analysis lies in the fact that a natural thermal gradient exists across human skin between the body's core temperature of close to 37.degree. C. and the skin surface temperature. Skin temperature is largely determined by skin capillary perfusion and temperature of the extraneous material in contact with the skin, e.g. air, fabric, solid material. The natural gradient is however small, sometimes no more than 1 degree Celsius per millimeter. However it can be substantially enlarged transiently or steady-state by the application of heat to the skin followed prior to or simultaneous to efficient heat withdrawal.
For analysis of the composition of subsurface layers, such as human skin for example, there are several advantages to using transmission spectrometry rather than emission spectrometry. In contrast to thermal emission spectrometry, in thermal gradient transmission spectrometry (whether transient or steady-state), the contribution of the immediate top surface layer to the overall transmission spectrum is relatively small because 1) it is the coldest layer and therefore contributes the smallest amount of blackbody radiation of all layers, 2) it is too thin to provide sufficient optical depth in many cases and 3) it's absorptive characteristics are not necessarily larger than those of deeper layers. Transient thermal transmission spectrometry has also been described by McClelland (5,070,242), and by some of the inventors of the present invention in co-pending U.S. patent application Ser. No. 08/544,267. This technique holds significant promise for the accurate, non-invasive measurement of in-vivo physiological constituents, if certain problems inherent in the interpretation of raw radiometric data provided thereby can be overcome. Further, the technique may be useful for other non-invasive metrologies, including but not necessarily limited to the measurement of materials through packages, e.g. food packages, and the measurement of blood pH.
To put these problems into perspective, it should be noted that thermal gradient spectrometry is similar in concept to conventional un-referenced single beam transmittance spectrometry with a simultaneous continually dimming light source and variable cuvette depth. From these facts, it is clear that several major problems exist in the interpretation of the raw radiometric data from an infrared source.
At any wavelength the total infrared emission It reaching a detector, for instance the detector of an infrared spectrometer, can be defined as: EQU I.sub.t =I.sub.i +I.sub.r +I.sub.s +(I.sub.0 *T),
where I.sub.i is the instrument background emission intensity, PA1 1) The utilization of a reference scan that is taken in a timely manner before the surface is cooled while the thermal infrared emission spectrum is substantially free of self-absorption, as taught by McClelland in U.S. Pat. No. 5,070,242. PA1 2) Alternatively, one may try to experimentally approximate the deeper layer gradient temperature emission by measuring the sample at different temperatures without a thermal gradient and subsequently use the one scan that gives the best approximation as judged from the results. PA1 3) As a further alternative, one can physically measure the surface temperature and the core temperature of the material, and thereafter derive an effective deeper layer radiation intensity by interpolation from the gradient temperature-depth profile. These temperatures can be converted to intensities by applying Planck's function. PA1 1) how to use wavelength ranges in a semi-empirical fashion such that the effective deeper gradient layer emission intensity and blackbody-equivalent emission temperature can be derived and can subsequently be used as the reference or standard intensity I.sub.0 in the calculation algorithm for transmittance; PA1 2) the importance, determination and elimination of the effects caused by variable contribution of surface emission in the determination and spectral calibration for 0% transmittance; PA1 3) the separation of deep layer radiation and surface emission; nor PA1 4) the utilization of wavelength ranges for the best possible spectral calibration for 100% transmittance calculation. PA1 a. Explicit, real time determination of I.sub.0 and I.sub.s. PA1 b. Fast, efficient calibration of infrared spectrometer. PA1 c. A relationship like the Beer-Lambert Law between light intensity and analyte concentration which is operative for thermal gradient spectrometry (TGS). PA1 d. Determination of a parameter which avoids having to measure path length explicitly. PA1 e. A means for determining a ratio of the concentrations of n analytes within a solution of analytes. PA1 a. Explicit, real time determination of I.sub.0 and I.sub.s. PA1 b. Explicit near real-time determination of I.sub.r and I.sub.i, thereby enabling the fast, efficient calibration of infrared spectrometric equipment. PA1 c. Determination of a parameter which avoids having to measure path length explicitly, which enables the definition of a relationship similar to the Beer-Lambert Law between light intensity and analyte concentration which is operative for TGS. PA1 d. From the foregoing relationship, a methodology for determining a ratio of the concentrations of n analytes within a solution of analytes. PA1 cooling an infrared transmissive mass; PA1 placing the infrared transmissive mass into a conductive heat transfer relationship with the tissue thereby to generate a transient temperature gradient in the tissue; PA1 detecting infrared emissions emanating from the tissue and passing through the infrared transmissive mass; PA1 providing output signals proportional to the detected infrared emissions; and PA1 sampling the output signals as the transient temperature gradient progresses into the tissue. PA1 1) how to use wavelength ranges in a semi-empirical fashion such that the effective deeper gradient layer emission intensity and blackbody-equivalent emission temperature can be derived and can subsequently be used as the reference or standard intensity I.sub.0 in the calculation algorithm for transmittance; PA1 2) the importance, determination and elimination of the effects caused by variable contribution of surface emission in the determination and spectral calibration for 0% transmittance; PA1 3) the separation of deep layer radiation and surface emission; and PA1 4) the utilization of wavelength ranges for the best possible spectral calibration for 100% transmittance calculation.
I.sub.r is the reflected emission, PA2 I.sub.s is the surface emission, PA2 I.sub.0 is the reference intensity, PA2 and T is the transmittance, generally defined as the ratio I/I.sub.0. PA2 c is the concentration of a constituent, such as glucose; PA2 and L is the optical path length.
The Problems of I.sub.0 and I.sub.s
One major problem in the interpretation of transient or steady-state thermal gradient subsurface spectrometric data is in the determination of the Reference Intensity I.sub.0. If one approximates the material to be analyzed as consisting of layers of equal or variable composition, then I.sub.0 is the total integrated emission from all the deep layers before modification by absorption in each individual layer. The reference intensity is produced while the thermal gradient exists, and is radiated out of the material under analysis, then convoluted with the instrument response function without the self-absorption effect of the cooler surface layer and without emission from the surface. In conventional spectrometry I.sub.0 is simplified as just the energy source intensity and approximated by a separate measurement. In transient or steady-state thermal gradient spectrometry the integral parts of I.sub.0 are the effective emission intensity, as well as the blackbody and specific spectral emissions coming from the deeper layers of the material during the thermal gradient.
Further, there is a surface emission I.sub.s, directly from the surface of the material under analysis. It consists of both blackbody and spectral emissions. A theoretically separate component from the surface is reflected emission I.sub.r. Surface emission is not part of I.sub.0 ; that is to say that it has not gone through the colder absorptive layer, and therefore it is not modified by self-absorption. Although surface emission is variable in intensity during the gradient as the surface is being cooled, it is possible to define an effective surface temperature during a time element.
The quality of I.sub.0 and I.sub.s measurements are as important as the quality of the sample intensity I measurements in determining the analytical accuracy of the constituent of interest. As the thermal gradient progresses to the deeper layers, the intensity and wavelengths of the emission peak of the initial blackbody radiation are dynamically changing. These layers are not only cooled in the process but their radiative emission is both substantially decreased and shifted to longer wavelengths. For non-intrusive in-vivo measurements, the actual effective temperature is inaccessible to physical measurements with a temperature probe. Nonetheless, it is necessary to know the effective deep layer emission or equivalent deep temperature because it is needed to calculate the effective deep, or reference intensity I.sub.0.
Transmittance is generally defined as the ratio T=I/I.sub.0. Accordingly, the quality of the I.sub.0 measurement or semi-empirical determination yields the resolution and accuracy of the resulting analytical constituent calculation. In addition to the emission from the material of interest there is the emission intensity I.sub.i from instrument components. Since I.sub.t =I.sub.i +I.sub.r +I.sub.s +(I.sub.0 *T), it becomes apparent that transmittance can only be calculated properly after the intensities emitted from the surface and from instrument components have been determined and subtracted.
By taking the ratio of I.sub.t /I.sub.0, with I.sub.0 being the result of an approximate determination, it is relatively easy to obtain an approximate transmittance spectrum that may be sufficiently accurate for less demanding applications, such as taught by McClelland U.S. Pat. No. 5,070,242. In fact for many applications, such as simple mixtures of relatively few components present in large relative amounts such a simple treatment may be perfectly satisfactory. With more critical metrology however, the use of this approximation leads to erroneous results. This is particularly true in applications with samples having relatively many components and which contain small amounts of one or more components that need to be measured accurately, such as clinical determinations of glucose or alcohol concentrations in body fluid. It is also true in applications that require larger percentages of components to be measured very accurately. Mathematically and physically, the problem lies in an incomplete elimination of all interfering emissions that originated either from any surface and/or from the deeper layers of the material during the thermal gradient.
The simplistic approach of taking a ratio will, by definition, give an exact transmittance spectrum only when all components that contribute to I.sub.t are exactly accounted for. This can only occur if and when the individual components can be determined independently from the superposition of the relative contributions from blackbody radiation and the emission/absorption depth dependent information. In conventional spectrometry the problem of sufficiently exact measurement of I.sub.0 and I.sub.t was largely solved when dual beam and/or highly stabilized energy source and detector systems were invented. A major limitation to accuracy improvements in conventional spectrometry is the fact that the reference measurement cannot be taken from the actual measurement energy while the measurement is taken without disturbing the measurement itself.
Neither the experimentally calculated deep emission nor the calculated surface emission are truly blackbody radiations, but rather are essentially blackbody radiations with specific spectral emission components superimposed onto them. It is appropriate, however, to treat them as blackbodies because the specific components are exactly the mirror images of the transmittance spectra of any layer of the material being analyzed. These spectral emission components are small in comparison to the effective absorption components induced by cooling and simply reduce the magnitude of the final transmission spectra without distorting them.
Several approximations for I.sub.0 may be useful in spectrometry less critical than in-vivo titer analysis. These include, but are not necessarily limited to:
What is really required however to enable the use of thermal gradient spectrometry as an accurate diagnostic technology is a novel method that reveals the effective I.sub.0 more accurately than any of the preceding approximations.
Because the prior art does not teach an accurate measurement methodology for I.sub.0, or even the importance thereof, the work of others does not, in general, teach:
The Problems of Calibration and Instrument Drift
All radiometers, including spectrometers, require calibration. Further, instrument settings can change over time, resulting in an error-inducing "drift". These facts are especially significant in transient thermal gradient transmission spectrometry, where a single "reading" is actually a continuous series of readings which result in a whole value. Ideally, a radiometer should be calibrated between individual measurements, and any drift corrected for. Since a single transient thermal gradient transmission spectrometric reading is an event measured in fractions of a second, and composes a number of individual measurements, a means for calibrating the instrument in near real time will render substantial improvements in instrument accuracy over previous thermal gradient transmission spectrometric methodologies. Similarly, a methodology for compensating, again in near real time, for any instrument drift which accumulates will significantly improve the accuracy of previous efforts at thermal gradient spectrometric constituent analysis.
The Optical Path Length Problem
Another major problem not contemplated by the prior art in the interpretation of transient or steady-state thermal gradient spectrometric data is in the determination of the optical path length. In conventional terms optical path length is equivalent to the cuvette dimension through which the light beam is traveling. In thermal gradient spectrometry there is no strictly defined cuvette thickness. In fact, effective cuvette thickness increases continually as the thermal gradient develops. The useful range though, is only a few optical depths, defined as the distance after which any intensity is reduced to 1/e by absorption. The equivalent in conventional terms would be a cuvette that increased in dimension while the measurement is being taken. According to Beer's law, which can be applied as the simplest case, ##EQU1## where: .beta. is the absorption coefficient;
It is immediately apparent, using this classical application of Beer's Law, that the concentration c cannot be determined if the path-length L is unknown. A methodology which allows the determination of a parameter whereby the concentration c of an analyte can be ascertained without the necessity for making an explicit determination of path-length L would finally enable transient thermal gradient spectrometry as a precision measure of such concentrations.
Summarizing the preceding discussion, thermal gradient spectrometry (either transiently or steady-state) holds promise as a methodology for obtaining in vivo optical spectra relating to the concentrations of analytes at depths to around 100-200 microns, and for determining those concentrations from the spectra. To fulfill this promise certain problems must be overcome and certain relationships defined. None of these solutions, unfortunately are taught or suggested by the cited reference. Specifically, what is required is:
A technique for the non invasive measurement of physiological constituents, specifically glucose, must address the problems that tissue is heterogeneous in composition with the tissue layers containing the physiological concentration of interest laying 20-150 microns below the surface. Furthermore, the technique must assure a safe and effective measurement that will not cause temporary or permanent damage to the surface or underlying tissues in the measurement site nor cause discomfort to the human subject. The technique must also overcome the potential problem that glucose and other physiological constituents are present in combination with a number of other similar molecules and must be distinguished for accurate quantification. Ideally such a technique would not require a high power source of infrared energy so that a device could be made portable and lightweight.